The physical, 3D Etch A Sketch seems to be baked, but this idea takes the concept a couple of steps further. This is a glass sphere, with silvery powder on its special inside surface, mounted on a base.

Inside, from the base, extends a probe for drawing or writing. The probe turns and telescopes
from a central joint, to etch the surface. Sunk into the middle of the base, is a fan to erase etchings by blowing a cloud of powder. Also inside is a light bulb to light the tracings and shine them onto the ceiling and walls.

One could sketch manually with a similarly jointed joystick, or messages and etchings could be input from a terminal. An automatic function would etch the time on one side of the globe and/or plot it backwards on the other side, to be illuminated onto the wall.

How you might implement this (aka my idea before I found out this one already existed):

A globe contains an arm, with stylus at some point on the surface of the sphere, and attached to a pivot at the centre of the sphere. From the pivot, a tube protrudes directly down, out the bottom of the sphere, to which two knobs are connected.

The bottom knob controls the theta coordinate. It rotates the stylus in the plane of the floor. It accomplishes this by simply rotating the metal tube inside of the globe, around the globe's vertical axis. In fact, it's not really a separte plastic piece, it's just a handle on the tube that gives you some torque so you can rotate it.

The second knob is mounted about an inch up from the first, and it is orthogonal to the plane of the floor. It moves the lever arm up and down, ALONG the lines of longitude. It could work by a simple drawbridge mechanism, rotating some conveyor belt which would attach to a wheel at the origin of the sphere.